What is expand log_{10}(x/(3y^3)) ?

The solution to expand log_{10}(x/(3y^3)) is log_{10}(x)-log_{10}(3)-3log_{10}(y)

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expand log_{10}(x/(3y^3))

expand

lo g_{10} (\frac{x}{3 y ^{3}})

lo g_{10} (x) - lo g_{10} (3) - 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{3 y ^{3}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{x}{3 y ^{3}}) = lo g_{10} (x) - lo g_{10} (3 y^{3})

= lo g_{10} (x) - lo g_{10} (3 y^{3})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (3 y^{3}) = lo g_{10} (3) + lo g_{10} (y^{3})

= lo g_{10} (x) - (lo g_{10} (y^{3}) + lo g_{10} (3))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (y^{3}) = 3 lo g_{10} (y)

= lo g_{10} (x) - (lo g_{10} (3) + 3 lo g_{10} (y))

- (lo g_{10} (3) + 3 lo g_{10} (y)) : - lo g_{10} (3) - 3 lo g_{10} (y)

= lo g_{10} (x) - lo g_{10} (3) - 3 lo g_{10} (y)

ln (\frac{1}{2}) + \frac{π}{6}

3 ln (a) + 2 ln (b)

ln (\frac{1 0 ^{7}}{1 0 ^{6}})

6 ln ∣ x + 1 ∣ + 3 ln ∣ x - 3 ∣

ln (6 \cdot 1 0^{6})

What is expand log_{10}(x/(3y^3)) ?
The solution to expand log_{10}(x/(3y^3)) is log_{10}(x)-log_{10}(3)-3log_{10}(y)